ANALISIS EFEKTIFITAS MODUL ANALISIS REAL MODEL APOS BERBANTUAN GEOGEBRA TERHADAP PEMAHAMAN KONSEPTUAL DAN REPRESENTASI VISUAL MAHASISWA PASCASARJANA

Abstract

This study aimed to examine the conceptual understanding and visual representation skills of Master's students in Mathematics Education on the topic of Real Number Sequences in the Real Analysis course, as well as to evaluate the effectiveness of a GeoGebra-assisted Real Analysis teaching module. The module integrated dynamic visualization and formal proofs on the topics of convergent sequences, monotonic sequences, and Cauchy sequences, and was accompanied by a compiled Student Activity Sheet (LAM). The learning process was conducted online with the support of a teaching assistant who provided guidance outside scheduled class hours. The participants were five Master's students in Mathematics Education, all of whom were mathematics teachers at junior and senior high schools, selected through purposive sampling after attending at least two meetings on the subject matter. The study employed a qualitative descriptive-exploratory approach. Research instruments included a conceptual understanding test, a visual representation assessment sheet, an open-ended performance-based task test, and semi-structured interviews. The findings indicated a significant improvement in students’ conceptual understanding and quality of visual representation. GeoGebra facilitated connections between the concepts of limits, convergence, monotonicity, and the Cauchy criterion, strengthened mathematical argumentation skills, and effectively bridged symbolic and graphical representations. Therefore, the GeoGebra-assisted Real Analysis module was effective in enhancing conceptual understanding and visual representation skills and has the potential to be adapted for other levels and topics in mathematics.